As far as I know, Bitcoin Faucet is funded by private donations of individuals who want the community to grow.
As for your idea, I think it is not bad at all. Many conventional sites (not affilated with bitcoins) make money like this. They make people click through a chain of subsites with ads. But since you want to use free mBTCs as an incentive you'll have to balance out money gained from ads and money given to those who click (you have to gain more than give).
I recommend you find something else to offer. I mean some sort of service useful for those who use bitcoins. The infrastructure is underdeveloped and there are so many things to improve. If you find something really useful for people, you'll make much money. Good luck.